ISSN (Print) 1226-1750 ISSN (Online) 2233-6656 Journal of Magnetics 20(3), 322-329 (2015) http://dx.doi.org/10.4283/JMAG.2015.20.3.322

Overlapped Electromagnetic Coilgun for Low Speed Projectiles

Hany M. Mohamed1, Mahmoud A. Abdalla2*, Abdelazez Mitkees, and Waheed Sabery

Electrical Engineering Branch, MTC College, Cairo, Egypt [email protected] [email protected]

(Received 20 February 2015, Received in final form 16 June 2015, Accepted 16 June 2015)

This paper presents a new overlapped coilgun configuration to launch medium weight projectiles. The proposed configuration consists of a two-stage coilgun with overlapped coil covers with spacing between them. The theoretical operation of a multi-stage coilgun is introduced, and a transient simulation was conducted for projectile motion through the launcher by using a commercial transient finite element software, ANSOFT MAXWELL. The excitation circuit design for each coilgun is reported, and the results indicate that the overlapped configuration increased the exit velocity relative to a non-overlapped configuration. Different configurations in terms of the optimum length and switching time were attempted for the proposed structure, and all of these cases exhibited an increase in the exit velocity. The exit velocity tends to increase by 27.2% relative to that of a non-overlapped coilgun of the same length. Keywords : electromagnetic launch, excitation circuit, lorentz force, overlapped coilgun

1. Introduction is not easy to obtain the main performance parameters and optimize the design [3]. Electromagnetic (EM) launch technology is a strong Sandia National Laboratories has succeeded in coilgun candidate to launch objects with high velocities over long design and operations by developing four guns with distances. A coilgun launcher is a specific application for projectiles ranging from 10 g to 5 kg and speeds of up to an electromagnetic launch that uses a moderate power 1 km/s, validating the computational codes and basis for excitation circuit [1]. A coilgun consists of discrete gun system control. In addition, coilguns use magnetic solenoidal coils that are connected end-to-end and are coupling to drive the current in the armature without wound around a hollow dielectric tube. A projectile inside requiring direct electrical contact between the barrel and this tube moves due to the presence of coupling between the projectile. This results in a long barrel lifetime that the coils and the armature. Capacitor bank circuits are will be useful for next-generation long-range artillery connected to the coils that are triggered sequentially to guns for land-based and naval platforms [4]. deliver current pulses into the coil's stages, and as the A coilgun launcher can be designed as a multi-stage current pulse travels through the coil’s winding, the structure. This kind of launcher can be referred to as a interaction between the magnetic field and the induced synchronous induction coilgun (SICG) or also a coaxial current within the armature (projectile) generates an axial coil launcher. It consists of a sequence of powered multi- force that moves the projectile along the barrel. A number turn drive coils that surround a barrel with a circular cross of parameters affect the performance and efficiency of the section through which a conducting armature passes [5]. coilgun including: the muzzle velocity, projectile peak The drive coils must be separately energized by the and average acceleration [2]. Although the working external source, which is controlled by switches that are principle of a coil gun is simple, the launch of a coil gun triggered to sequentially deliver current pulses into the is a complex electromagnetic transient process, and so it coil stages. The time to turn the switches on and off must be governed by the position of the armature [6]. This type of launcher has several advantages that result ©The Korean Magnetics Society. All rights reserved. in a higher acceleration, including no drop in acceleration *Corresponding author: Tel: +2-01118750114 Fax: +2-01118750114, e-mail: [email protected] as the mass of the projectile increases, a higher peak

© 2015 Journal of Magnetics Journal of Magnetics, Vol. 20, No. 3, September 2015 − 323 − pressure on the projectile and smaller differences between the average and peak pressure. The analytical approach for an inductive coilgun is relatively complex due to the time-varying mutual inductances between the driver coils and the projectile in the transient launch process. Hence, it is necessary to rely on finite element software or a numerical approach to design a coilgun that can achieve good launch characteristics [7]. In this paper we introduce a new configuration for a multi-stage coilgun that is based on an overlap between Fig. 1. (Color online) Forces that exist on the stator and arma- two cascaded coilgun stages. This configuration is pro- ture coaxial coils for a single stage coilgun. posed in order to achieve a higher launch velocity for a projectile with the same coilgun length. The theoretical projectile, (Jaφ) is the radial armature current density and concepts of the proposed overlapped structure are intro- (Bsr) is the stator radial magnetic field. Hence, the speed duced, and the performance of the new configuration is inside of the projectile resulting from this force can be examined and compared to that of a conventional (non- calculated as [6] overlapped) coilgun. An extensive study was carried out dv dM m ------a I I ------as- to validate the results, and the simulation of the projectile a dt = a s dz (2) movement through the coilgun is carried out by using the finite element method. dz v ----- a = dt (3) 2. Theory where (ma) is the mass of the armature, (va) is the velocity of the armature, and (Ia, Is) are the induced armature and 2.1. Basic Coilgun Concept stator coil currents, respectively. (z) is the displacement of The electromagnetic coil launcher structure is shown in the armature and (Mas) is the mutual inductance between Fig. 1, and as is shown in the figure, it consists of stator the armature and the stator coil [6]. coil and an armature that moves along the stator coil axis. As shown in the figure, the armature is the projectile 2.2. Multi stage Coil Gun itself, and the stator current density (Js) circulates around In the case of the multi stage coilgun, the analysis can the axis. This current induces a magnetic field inside the be carried using the Current Filament Method (CFM), as armature (Ba), and accordingly, a current density (Ja) is shown in Fig. 2. The projectile and conductive parts of induced in the armature that results in turn in a magnetic the coil are divided into elementary elements (m and n) field around the stator (Bs). The force that affects the within which the projectile can be assumed to be a point projectile inside of the electromagnetic coil is shown in projectile. Hence, the current distribution is uniform. Fig. 1, and the driving force (F) in the coil launcher is the Next, a numerical field computation is used to calculate Lorentz Force [8, 9]. The force (F) can be decomposed the value of the forces that are applied on the projectile into a propulsive (axial) force (Fz) and a radial force (Fr) by determining the flux distribution, magnetic field and that exist on both the armature and the stator. velocity that act on the projectile anywhere inside of the The radial forces of the coilgun that are induced on the system for each small section. Finally, the current filament both stator and the armature are in opposite directions. associated with each volume element and its correspond- These opposing radial forces center the armature inside ing electrical parameters are calculated. the stator coil, making a contactless launch possible. The velocity of the projectile can be calculated using Hence, the projectile is centered and no friction occurs Eq. (3), where the force exerted on the projectile can be between the projectile and the stator walls, and thus, the calculated as [10] radial forces are balanced. Accordingly, the motion of the m projectile inside of the stator is mainly a result of the dva dMasi ma------= ∑ IaiIsi------(4) armature axial force that affects the projectile. This force dt i = 1 dz can be mathematically expressed as where Faz = Jaϕ × –Bsr (1) th Iai : Armature current for the i element point where (Faz) is the armature axial force that pushes the projectile. − 324 − Overlapped Electromagnetic Coilgun for Low Speed Projectiles − Hany M. Mohamed et al.

Fig. 2. (Color online) Schematic diagram of the CFM of a coilgun. Fig. 3. (Color online) Coilgun layout (a) two-stage coilgun. (b) two-stage overlapped coilgun. th Isi : Stator current for the i element point projectile. th Zpi : position along the z axis of the i element point projectile. muzzle point. Therefore, we have to select the best position th Masi : Mutual inductance between the i element point to launch the projectile in order to obtain the highest projectile and the coil (stator). muzzle velocity. 2. Studying the effect of the flux linkage between the The knowledge of the magnetic field at an arbitrary coil and armature to ensure the best muzzle velocity of place (Zpi) allows for a simplified form of the mutual the projectile. inductance to be be written as 3. An inversely proportional relationship is observed N2µA Z ()Z l between the length of the coil and the muzzle velocity of M pi pi – asi = ------– ------(5) the projectile, so the coil length needs to be optimized to 2l a2 Z a2 ()lZ 2 + pi + – pi obtain a better muzzle velocity. From the velocity definition for the finite length projectile, 4. The effect of the number of turns of the coil, applied a numerical code should be used to solve the projectile voltage and current pulse must be investigated and velocity, flux linkage and mutual inductances. The transient optimized in order to achieve the desired muzzle velocity. finite element method is used, and the ANSYS MAXWELL 5. Finally, the material of the projectile has a big effect commercial software is employed during this simulation. on its velocity. Accordingly, it is necessary to choose the In our work, mutual coupling can be further improved best material to ensure a suitable muzzle velocity. with two overlapping stages. This introduces a higher In our work, two models were designed, and their degree of freedom in the designing of a multi-stage performance is evaluated by using using the ANSOFT coilgun that can achieve a higher exit velocity, as will be MAXWELL transient finite element commercial software. explained in the following section. The first model consists of a two-stage coilgun with each coil of length “L1” and “L2” with spacing “S” 3. Structure and Results between them, as shown in Fig. 3(a). The second model is a two-stage overlapped coilgun where the spacing between 3.1. Structure the two stages is covered by the overlapped coil with As previously mentioned, the structure proposed in our length “L3,” as shown in Fig. 3(b). Each coil has its own work is that of an overlapped coilgun. This structure was number of turns, and the end of the projectile is placed at investigated and is compared to a conventional multi the zero “Z” axis as the initial position. It is worth stage coilgun. Design started by optimizing the single- commenting that the starting position of the projectile has stage coilgun length and the number of turns [11]. The passed many optimizations, and the projectile is a hollow detailed parameters of the optimization are explained in aluminum cylinder with an inner radius of 43 mm, outer Ref. [12] as follows: radius of 51 mm and weight of 0.51 Kg. A band was 1. The initial position of the projectile is a very important added in the simulation to give the projectile the oppor- parameter to know because it can affect the velocity of tunity to move along the path desired inside the barrel the projectile during its path along the barrel until the until leaving it. Journal of Magnetics, Vol. 20, No. 3, September 2015 − 325 −

Fig. 4. (Color online) (a) Excitation circuit for the two-stage coilgun. (b) excitation circuit for the two-stage overlapped coilgun.

3.2. Excitation circuit relative to the non-overlapped one. This is carried out in In this section, we present the excitation circuit that two steps, the first one involves investigating the effect of delivers sufficient current to produce the required magnetic the coil spacing and the second one consists of changing field to push the armature forward. The excitation circuit the used coil length itself. was designed as a moderate power circuit and is used in our work to provide a discharging pulse. The initial energy 3.3.1. Effect of Spacing: is stored in a capacitor bank with an equivalent value of 2 The effect of the spacing “S”, and hence the overlap mF. The circuit editor of the ANSOFT MAXWELL com- length “L3”, is the main cause for coupling between the mercial software is used to validate the design. two stages of the coilgun. Hence, the exit velocity of the As shown in Fig. 4 the excitation circuit was imple- muzzle is simulated for ten different possible cases of S. mented during the discharge phase as the initial stored The two aligned coils are kept constant with a length of voltage in the capacitor bank was 5000 V. A freewheeling 60 mm and 120 turns. Accordingly, the length (L3) of the diode is connected across each winding to prevent the overlapped coil and its number of turns varies in each discharged pulse from oscillating and to ensure its smooth case. The results are thus recorded with spacing between decay with time. A pulsed switch was also added to the two stages that starts from 5 mm to 50 mm with 5 provide precise timing for the switch after the projectile mm steps in each case. We will choose only two of these leaves the first coil stage. The naming of the windings in to be further discussed in the details, and we finally the circuit editor must be the same in the finite element represent the data figure that shows all of the results in a simulator to be synchronized with each other while comparison between the two-stage coilgun and the two- importing it from another circuit editor. As shown in Fig. stage overlapped coilgun. 4(a), winding 1 is named to be synchronized with the first In the first chosen case, the spacing (S) is detected as coil while winding 2 is named to be synchronized with 25 mm between the first and second coil while the second the second coil in the finite element simulator. As shown case spacing (S) is detected as 40 mm between the first in Fig. 4(b), the naming is the same for the windings as in and second coil. For the first focused case, the non Fig. 4(a), except with the addition of winding 3 that is to overlapped configuration is shown in Fig. 5(a). After 1 be synchronized with the overlapped coil that is added ms, the second stage is excited by its own supply circuit over spacing between the two coils, as previously men- that supports the magnetic field of first coil in order to tioned in Fig. 3(b). increase the velocity of the projectile, resulting in an exit velocity that reaches 142.6 m/s after 3.1 ms from dis- 3.3. Results charge. On the other hand, the overlapped configuration In the results section, we investigate how the overlapped in Fig. 5(b) has a length of 80 mm for the overlapped coil section can improve the performance of the coilgun (L3), where it covers two cascaded coils by 27.5 mm up − 326 − Overlapped Electromagnetic Coilgun for Low Speed Projectiles − Hany M. Mohamed et al.

Fig. 5. (Color online) (a) Two-stage coilgun with 25 mm spacing between the cascaded coils. (b) two-stage overlapped coilgun with 80 mm of overlapped coil covering the spacing between the cascaded coils.

ration The length of the overlapped coil (L3) remains 80 mm, as shown in Fig. 7(b). In this case, the dimensions are the same for the length, width and number of turns for the three coils, except that the spacing between the two aligned stages is raising to 40 mm. After 1.8 ms, the second stage is excited to increase the velocity of the projectile, which leaves the first stage completely with a velocity of 97.6 m/s after 2.2 ms, resulting in an exit velocity that reaches 132.1 m/s after 3.1 ms from dis- charge. On the other side, the velocity that is recorded for Fig. 6. (Color online) Velocity profile results for the two-stage the projectile after 3.2 ms was of 163.1 m/s in an over- coilgun and two-stage overlapped coilgun with 25 mm spac- lapped configuration which is a 23.46% increase in the ing between the cascaded coils. velocity when compared to the cascaded two-stage coilgun, as shown in Fig. 8. The projectile velocity for the two-stage coilgun and the and down. This overlapped coil has its own supply circuit two-stage overlapped coilgun versus the spacing is shown that is excited after 1 ms to support a projectile until in Fig. 9, where the spacing varies from 5 mm to 50 mm. reaching the second coil, which is excited after 1.5 ms. In The results of the figure confirm that the overlapped this case, the projectile is recorded to reach the end of configuration has a better response than the conventional barrel after 3 ms with an exit velocity nearly equal to 167 one. It is obvious that the spacing between the two m/s. Thus, there is a 17.1% increase in velocity in the cascaded stages is essential to increase the velocity. The case with the overlapped coilgun relative to the cascaded best result is thus achieved for a separation of 35 mm two-stage coilgun. To explain this improvement in the where the exit velocity increases from 124.2 m/s to 158 exit muzzle velocity, the projectile velocity profile in the m/s (27.2%). two cases is simulated, as shown in Fig. 6. In the first two Table 1 summarizes the ten cases that have been studied, milliseconds, the behavior of the two models remains the showing the spacing, length and exit velocity of each same until the effect of the overlapped coil appears, overlapped case. Finally, we can say that the overlapped which makes a difference in the velocity. case can achieve a better exit velocity relative to the non- The second case of the geometry that was chosen for overlapped coilgun. focus is shown in Fig. 7(a) for the non overlapped con- The effect of the overlapped length is also discussed for figuration and in Fig. 7(b) for the overlapped configu- the 40 mm spacing between the aligned stages (as the Journal of Magnetics, Vol. 20, No. 3, September 2015 − 327 −

Fig. 7. (Color online) (a) Two-stage coilgun with 40 mm spacing between the cascaded coils, (b) two-stage overlapped coilgun with 80 mm of overlapped coil covering the spacing between the cascaded coils.

Table 1. Results for the ten cases studied for the overlapped coilgun. Spacing Overlapped coil length Exit velocity (mm) (mm) (m/s) 5 20 160.8 10 20 158 15 20 158.9 20 60 147.3 25 80 166.9 30 60 151.4 35 60 158 Fig. 8. (Color online) Velocity profile results for the two- 40 80 163.1 stage coilgun and two-stage overlapped coilgun with 40 mm 45 80 158 spacing between the cascaded coils. 50 60 150.3

optimum spacing between the two aligned coils) and a number of results were recorded for different values of the overlapped, length starting from 5 mm to 35 mm with a 5 mm increment in each of the recorded results. The detailed results are shown in Fig. 10, where the muzzle velocity decreases from 167.2 m/sec to 155.5 m/sec as the overlapped length increases. To illustrate our idea of the effect of the overlapped coil through our work, the two cases that were studied are re- plotted within the position to determine the position for which the overlapped length takes place. For the first Fig. 9. (Color online) Velocity comparison between the two- chosen case, which is shown in Fig. 11, the two models stage coilgun and two-stage overlapped coilgun. had the same velocity profile for the first 40 mm of the − 328 − Overlapped Electromagnetic Coilgun for Low Speed Projectiles − Hany M. Mohamed et al.

Fig. 10. (Color online) Muzzle velocity of the projectile vs the overlapped length covering the cascaded coils. Fig. 13. (Color online) Detailed results for the velocity of the projectile for different aligned coil length in the case of an overlapped coilgun.

shown in Fig. 12, to show the effect of the overlapped length as it appears beneath 100 mm of its journey inside of the barrel. Finally, we can comment that the overlapped case can achieve a better muzzle velocity relative to the non- overlapped coilgun. This improvement is clearer where the spacing between the two main coils increases as a result of the overlap in the coil contribution. However, the Fig. 11. (Color online) Velocity results for the two-stage coil- gun and two-stage overlapped coilgun with 25 mm spacing overlapped configuration introduces better results. between the cascaded coils. 3.3.2. Effect of the Change in the Coil length The previous section described how the overlapped total journey of the projectile, but after 1 ms, overlapped coilgun achieves better results than a conventional con- stage is excited by its own supply circuit supporting the figuration. The previous results were based on the selected magnetic field of first coil thereby increasing the velocity aligned coil length of 60 mm. In this section, we will thus of the projectile for overlapped case. The curve of the study the effect of changing the length of the aligned coils velocity begins to move up, and it moves away from the “L1 and L2” for the overlapped structure on the velocity velocity curve of the non-overlapped coilgun. of the projectile. The best overlapped distance was “OL” Similar to what was done for the first case, the second = 5 mm, spacing = 40 mm. The length of the aligned coils case (for S = 40 mm) is re-plotted with the position, as

Fig. 12. (Color online) Velocity results for the two-stage coil- Fig. 14. (Color online) Detailed velocities for the different coil gun and two-stage overlapped coilgun with 40 mm spacing lengths starting from 40 mm to 70 mm for the non-overlapped between the cascaded coils. coilgun. Journal of Magnetics, Vol. 20, No. 3, September 2015 − 329 −

Table 2. Projectile's muzzle velocity for different lengths of seven cases that were studied. From Fig. 15, we can claim aligned coils for an overlapped/non-overlapped medium caliber that the drop in the velocity for the longer coil is reduced coilgun. in the case of the overlapped configuration, and this can Overlapped Non Overlapped be explained to be a consequence of the compensation of Length of Configuration Projectile’s Configuration Projectile’s the reverse flux linkage in the two main coils by a aligned coils muzzle velocity muzzle velocity forward flux linkage of the overlapped coil. This point [mm] [m/sec] [m/sec] needs to be investigated, and also the effect of the current 40 169.4 149.1 flow through the overlapped coil should be further studied. 45 169.3 148.4 50 168.8 141 4. Conclusion 55 168.1 137.6 60 167.2 132.1 A new configuration has been introduced for a coilgun. 65 162.2 123.1 The theoretical concept of the proposed configuration is 70 160.2 110.9 discussed, and the design of the coilgun excitation circuit was introduced. The proposed overlapped coilgun launcher has been tested for ten different cases with different spacing and length of the overlapped coil. The results indicate that for each of the ten cases, the exit velocity of the overlapped coilgun was better than the exit velocity of non overlapped case with the same length (up to 33% increase). Moreover, the proposed overlapped coilgun can be applied for multi-stage configurations for higher weighted projectiles. References

Fig. 15. (Color online) Velocity comparison between the two- [1] O. Gurhan, M.Sc. Thesis, Monterey, California (2001). stage coilgun and two-stage overlapped coilgun for the same [2] D. C. Lamppa, C. J. Garasi, A. C. Robinson, T. V. Russo, spacing between the aligned coils. D. N. Shirley, and M. S. Aubuchon, USA Patent, Sandia National Labs, USA (2008). “L1 and L2” will vary seven times from 40 mm to 70 [3] S. Liu, J. Ruan, D. Huang, and Z. Wan, IEEE IPEMC 09, mm, with an increase of 5 mm each time. 845 (2009). [4] R. J. Kaye, IEEE Tran. Magn. 41, 194 (2005). The detailed results for all cases studies are shown in [5] W. Liu, C. Yanjie, Y. Zhang, J. Wang, and D. Yang, IEEE Fig. 13. There is an inversely proportional relation between Trans. Plasma Sci. 39, 100 (2011). the length of the aligned coils and the velocity of the [6] Y. Zhang, K. Liu, J. Liao, Y. Zhang, C. Wu, and Y. Hu, projectile: as the length of aligned coils increases, the 16th Int. EML Symp. 1, 100 (2012). velocity of the projectile decreases. [7] L. Guo, N. Guo, S. Wang, J. Qiu, J. Guo Zhu, Y. Guo, For the sake of comparison, the results for the detailed and Y. Wang, IEEE Energy Con. Congress and Exp. 1, velocities of the non-overlapped configuration are plotted 234 (2009). in Fig. 14 for each of the studied cases, starting from 40 [8] K. E. Eeinhard, M.Sc. Thesis, University of Texas, Aus- mm to 70 mm. It is obvious that, as presented before, the tin (1992). increase in the length of the aligned coils will decrease [9] M. Barry, IEEE Trans. Mag. 29, 701 (1993). the muzzle velocity. Moreover, a comparison of Figs. 13 [10] S. Liu, J. J. Ruan, P. Ying, Y. J. Zhang, and Y. D. Zhang, and 14 in terms of the muzzle velocity indicates that the IEEE Trans. Plasma Sci. 39, 382 (2011). overlapped configuration not only increase the muzzle [11] H. M. Mohamed, M. A. Abdalla, A. A. Mitkees, and W. velocity but also preserve the velocity the profile from S. Sabery, ICET 1, 1 (2014). [12] H. M. Mohamed, M.Sc. Thesis, MTC College, Egypt deformation. The comparison of the muzzle velocity of (2014). the projectile can be plotted more clearly in Fig. 15. Also, the values from the figure are presented in Table 2 for the